Abstract:In this paper, we use a characterization of $R$-modules $N$ such that $fd_RN = pd_RN$ to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting $N$ to be the $dth$ local cohomology functor of $R$ with respect to the maximal ideal where $d$ is the Krull dimension of $R$.
Keywords: injective, precovers, preenvelopes, canonical module, Cohen-Macaulay, \newline $n$-Gorenstein, resolvent, resolutions
AMS Subject Classification: 13C14, 13D45, 13H10, 18G10